Hi Op,
Switzerland has a bilateral tax agreement with the US. In general, but much depends on what you and your spouse earn collectively and whether you will file jointly in the US; if so, your taxes owed in Switzerland are typically lower than you tax obligation in the US.
Taxes paid in Switzerland are typically offset to those owed in the US. Much depends upon your income and how you file. Probably best to consult a tax consultant.
Mullhollander gives great advice and is an accountant. Maybe PM him?